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Continuous-time mean-variance portfolio selection with liability and regime switching

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  • Xie, Shuxiang
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    Abstract

    A continuous-time mean-variance model for individual investors with stochastic liability in a Markovian regime switching financial market, is investigated as a generalization of the model of Zhou and Yin [Zhou, X.Y., Yin, G., 2003. Markowitz's mean-variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim. 42 (4), 1466-1482]. We assume that the risky stock's price is governed by a Markovian regime-switching geometric Brownian motion, and the liability follows a Markovian regime-switching Brownian motion with drift, respectively. The evolution of appreciation rates, volatility rates and the interest rates are modulated by the Markov chain, and the Markov switching diffusion is assumed to be independent of the underlying Brownian motion. The correlation between the risky asset and the liability is considered. The objective is to minimize the risk (measured by variance) of the terminal wealth subject to a given expected terminal wealth level. Using the Lagrange multiplier technique and the linear-quadratic control technique, we get the expressions of the optimal portfolio and the mean-variance efficient frontier in closed forms. Further, the results of our special case without liability is consistent with those results of Zhou and Yin [Zhou, X.Y., Yin, G., 2003. Markowitz's mean-variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim. 42 (4), 1466-1482].

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 45 (2009)
    Issue (Month): 1 (August)
    Pages: 148-155

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    Handle: RePEc:eee:insuma:v:45:y:2009:i:1:p:148-155

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    Web page: http://www.elsevier.com/locate/inca/505554

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    Keywords: Continuous-time Mean-variance model Asset-liability management Markov chain Linear-quadratic control;

    References

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    1. Boyle, Phelim & Draviam, Thangaraj, 2007. "Pricing exotic options under regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 267-282, March.
    2. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
    4. Andrea Consiglio & Flavio Cocco & Stavros A. Zenios, 2001. "Asset and Liability Modeling for Participating Policies with Guarantees," Center for Financial Institutions Working Papers 00-41, Wharton School Center for Financial Institutions, University of Pennsylvania.
    5. Norberg, Ragnar, 1999. "Ruin problems with assets and liabilities of diffusion type," Stochastic Processes and their Applications, Elsevier, vol. 81(2), pages 255-269, June.
    6. Naik, Vasanttilak, 1993. " Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns," Journal of Finance, American Finance Association, vol. 48(5), pages 1969-84, December.
    7. Siu, Tak Kuen, 2008. "A game theoretic approach to option valuation under Markovian regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1146-1158, June.
    8. Chiu, Mei Choi & Li, Duan, 2006. "Asset and liability management under a continuous-time mean-variance optimization framework," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 330-355, December.
    9. Hyeng Keun Koo, 1998. "Consumption and Portfolio Selection with Labor Income: A Continuous Time Approach," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 49-65.
    10. Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2006. "A path integral approach to asset-liability management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 404-416.
    11. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
    12. Kyriakos Chourdakis, 2000. "Stochastic Volatility and Jumps Driven by Continuous Time Markov Chains," Working Papers 430, Queen Mary, University of London, School of Economics and Finance.
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    Cited by:
    1. Delong, Lukasz, 2010. "An optimal investment strategy for a stream of liabilities generated by a step process in a financial market driven by a Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 278-293, December.
    2. Yao, Haixiang & Li, Zhongfei & Chen, Shumin, 2014. "Continuous-time mean–variance portfolio selection with only risky assets," Economic Modelling, Elsevier, vol. 36(C), pages 244-251.
    3. Yao, Haixiang & Lai, Yongzeng & Li, Yong, 2013. "Continuous-time mean–variance asset–liability management with endogenous liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 6-17.

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